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Properties of Solids:SuperconductivityExperiment objectives:study behavior of a high temperature superconducting material Yttrium-Barium-Copper-Oxide (YBCO,Y Ba2Cu3O7) in magnetic ﬁeld,measure the critical temperature for a phase tran-sition in a superconductor.HistorySolids can be roughly divided into four classes,according to the way they conduct electricity.They are:Met-als,Semiconductors,Insulators and Superconductors.The behavior of these types of materials is explainedby quantum mechanics.Basically,when atoms form a solid,the atomic levels of the electrons combine toform bands.That is over a ﬁnite range of energy there are states available to electrons.Since only oneelectron can occupy a given state,the Pauli Exclusion Principle,electrons will ﬁll these states up tosome maximum,the Fermi Energy:Ef.A solid is a metal if it has an energy band which is not full;theelectrons are then free to move about,making a metal a good conductor of electricity.If the solid has aband which is completely full,with an energy gap to the next band,that solid will not conduct electricityvery well,making it an insulator.A semiconductor is between a metal and insulator:while it has a full band(the valence band),the next band (the conduction band) is close enough in energy and so that the electronscan easily reach it.Superconductors are in a class by themselves.They can be metals or insulators at roomtemperature.Below a certain temperature,called the critical temperature,the electrons ”pair” together(in Cooper pairs) and travel through the solid without resistance.Current in a superconductor below thecritical temperature will travel indeﬁnitely without dissipation.Superconductivity was discovered in 1911 by H.Onnes.He discovered that simple metals (Pb,Nb)superconduct when placed in liquid helium (4 K).This was an important discovery,but the real excitementcame in 1986 when Swiss scientists discovered that certain ceramics would superconduct at 35 K.Severalgroups later discovered materials that would superconduct at temperatures up to 125 K.These materials arecalled high temperature superconductors (HTS).Their discovery was a breakthrough,because this meansthat these superconductors will work in liquid nitrogen (at 77 K),which is relatively cheap and abundant.Some fascinating facts about superconductors:they will carry a current nearly indeﬁnitely,without resis-tance.Superconductors have a critical temperature,above which they lose their superconducting properties.Another striking demonstrations of superconductivity is the Meissner eﬀect.Magnetic ﬁelds cannotpenetrate superconducting surface,instead a superconductor attempts to expel all magnetic ﬁeld lines.It isfairly simple to intuitively understand the Meissner eﬀect,if you imagine a perfect conductor of electricity.If placed in a magnetic ﬁeld,Faraday’s Law says an induced current which opposes the ﬁeld would be setup.But unlike in an ordinary metal,this induced current does not dissipate in a perfect conductor.So,thisinduced current would always be present to produce a ﬁeld which opposes the external ﬁeld.In addition,microscopic dipole moments are induced in the superconductor that oppose the applied ﬁeld.This inducedﬁeld repels the source of the applied magnetic ﬁeld,and will consequently repel the magnet associatedwith this ﬁeld.Thus,a superconductor will levitate a magnet placed upon it (this is known as magneticlevitation).Safety• Wear glasses when pouring liquid nitrogen.Do not get it on your skin or in your eyes!• Do not touch anything that has been immersed in liquid nitrogen until the item warms up to the roomtemperature.Use the provided tweezers to remove and place items in the liquid nitrogen.1Figure 1:The superconducting disk with leads.• Do not touch the superconductor,it contains poisonous materials!.• Beware of the current leads,they are carrying a lethal current!Experimental procedureEquipment needed:YBCO disc,tweezers,styrofoam dish,small magnet.Magnetic Levitation (the Meissner eﬀect)1.Place one of the small magnets (provided) on top of the superconducting disc at room temperature.Record the behavior of the magnet.2.Using the tweezers,place the superconducting disk in the styrofoam dish.Attach the thermocoupleleads (see diagram) to a multimeter reading on the mV scale.Slowly pour liquid nitrogen over thedisk,ﬁlling the dish as much as you can.The nitrogen will boil,and then settle down.When themultimeter reads about 6.4 mV,you are at liquid nitrogen temperature (77 K).3.After the disc is completely covered by the liquid nitrogen,use the tweezers to pick up the providedmagnet and attempt to balance it on top of the superconductor disk.Record what you observe.4.Try demonstrating a frictionless magnetic bearing:if you carefully set the magnet rotating,you willobserve that the magnet continues to rotate for a long time.Also,try moving the magnet across thesuperconductor.Do you feel any resistance?If you feel resistance,why is this.5.Using tweezers,take the disk (with the magnet on it) out of the nitrogen (just place it on side of disk),allowing it to warm.Watch the thermocouple reading carefully,and take a reading when the magnetfails to levitate any longer.This is a rough estimate of the critical temperature.Make sure you recordit!6.Repeat the experiment by starting with the magnet on top of the superconductor disc and observe ifthe magnet starts levitating when the disk’s temperature falls below critical.Measuring resistance and critical temperatureWe will measure the resistance by a four probe method,as a function of temperature.Using four probes(two for current and two for voltage) eliminates the contribution of resistance due to the contacts,and isgood to use for samples with small resistances.Connect a voltmeter (with 0.01 mV resolution) to the yellowwires.Connect a current source through an ammeter to the black wires.Place a current of about 0.2 Amps2(200 mA) through black leads.Note:DO NOT EXCEED 0.5 AMP!!!!At room temperature,youshould be reading a non-zero voltage reading.1.With the voltage,current and thermocouple leads attached,carefully place disk in dish.Pour liquidnitrogen into the dish.Wait until temperature reaches 77 K.2.With tweezers,take disk out of nitrogen and place on a side of the dish.Start quickly recording thecurrent,voltage and thermocouple readings as the disk warms up.When superconducting,the disk should have V=0 (R=0).At a critical temperature,you will see a voltage (resistance) appear.3.Repeat this measurement several time to acquire signiﬁcant number of data points near the criticaltemperature (6.4-4.5 mV).Make a plot of resistance versus temperature,and make an estimate of thecritical temperature based on this plot.Resistivity of another material:silicon (a semiconductor)1.Place a piece of silicon between alligator clips,attached to a multimeter reading resistance (kΩ to MΩrange).Treat it gently- it breaks easily.Record the room temperature resistance.2.Dunk the silicon in liquid nitrogen.Wait until it stops boiling.Record the resistance at this lowtemperature (≈77 K).3.Take the silicon out of the nitrogen and carefully set it down.Record the resistance as the temper-ature increases.Make a plot of the measured resustance vs temperature.Compare two plots for thesuperconductor and the silicon,and explain the diﬀerences.3